Math 442: Differential Geometry of Curves and Surfaces

David Dumas

University of Illinois at Chicago
Fall 2010

Unduloid
The unduloid, a surface of rotation of constant (nonzero) mean curvature.

General information

CRN 32336 (undergraduate), 32337 (graduate)
Lectures MWF 11:00 - 11:50am in Stevenson 215
Text Differential Geometry of Curves and Surfaces by Manfredo do Carmo (see also: list of errata)
ISBN-13: 978-0-13-212589-5
Instructor David Dumas (ddumas@math.uic.edu)
Office hours Mondays and Wednesdays 2-3pm in SEO 503
Exam week office hours Monday, Dec 6, 1-4pm
Homework Policies Homework problems will be assigned on Mondays and Wednesdays, and occasionally on Fridays.
Homework is due by 4pm on the first lecture day of each week (usually Monday) and can be turned in during lecture or directly to the grader's mailbox (Jonah Gaster) in the mailroom on the 3rd floor of SEO.
The list of challenge problems (see course materials) will be updated on a regular basis; you must complete four of these problems during the semester, with at least two of them submitted before the midterm exam.
Late homework will not be accepted.
You can discuss the homework with other students, but you must write (and understand!) your own solutions.
The homework problems depend on material from both the assigned reading and the lectures. Do not leave the problem sets or reading to the last minute!

Course Materials

These documents are available for download in PDF format.

Important Dates

There will be one midterm exam and a cumulative final exam.
Curve Day Wed, Sep 22 SEO 612
Midterm Exam Wed, Oct 13 SH 215
Surface Day Wed, Nov 24 SEO 612
Final Exam Thurs, Dec 9, 10:30am-12:30pm SH 215

Grading

Your course grade will be determined on the following basis:
Homework 30%
Midterm Exam 30%
Final Exam 40%

When computing your homework grade, the lowest weekly homework score will be dropped, and the remaining scores will be averaged with your challenge problem scores. (That is, each challenge problem is worth as much as a weekly homework assignment!)

Assignments

Reading

Unless otherwise noted, all reading assignments refer to the textbook, Differential Geometry of Curves and Surfaces by Manfredo do Carmo.
Date Reading
Nov 5 Sections 4.4-4.5
Oct 27 Sections 3.5 and 4.1-4.3
Oct 18 Sections 3.1-3.3 and chapter 3 appendix
Oct 6 Sections 2.5-2.6
Sep 27 Section 2.4
Sep 20 Section 2.3 and chapter 2 appendix
Sep 13 Sections 2.1-2.2
Aug 23 Chapter 1

Homework

The list of homework problems was last updated on Monday, November 22. The most recently assigned problems are shown in green.

Hwk # Due Problems
14 ** not collected ** Section 4.6: 1,2,4,5
13 Wed, Dec 1 Problems from Lecture 39.
12 Mon, Nov 22 Problem from Lecture 36.
Section 4.4: 20a
11 Mon, Nov 15 Section 4.3: 3, 9
Section 4.4: 1, 2, 5, 8
10 Mon, Nov 8 Section 3.5: 3
Section 4.3: 1, 2, 5, 8
9 Mon, Nov 1 Section 3.2: 2, 5, 17
Section 3.3: 5, 6, 20
8 Mon, Oct 25 Section 2.5: 7, 9, 10, 12
Section 3.2: 3, 8
7 Mon, Oct 11 Section 2.3: 1, 4
Section 2.4: 1, 3, 12, 15, 20
6 Mon, Oct 4 Problems from Lecture 15.
Section 2.2: 17 (Hint: Read section 2.3)
5 Mon, Sep 27 Section 2.2: 1, 2, 3, 5
4 Mon, Sep 20 Problem from Lecture 10.
Problems from Lecture 9.
3 Mon, Sep 13 Problems from Lecture 7.
Problem from Lecture 8.
2 Wed, Sep 8 Additional problems from Lecture 5.
Section 1.5: 5, 12, 14
1 Mon, Aug 30 This corrected version of problem 4 from section 1.3.
Section 1.4: 8
Section 1.5: 2, 4, 7

Online Resources

These online tools (java applets, etc.) complement the material from the textbook and lectures.
Up: Home page of David Dumas